Riemann Sum Right Problem

Question

Evaluate the Riemann Sum Right in the interval [a,b] with n sections. f(x) = - 5x + 6

1. What is the Riemann Sum - Right when n is 10?

2. What is the Riemann Sum - Right when n is 100?

3. What is the Riemann Sum - Right when n approaches infinity?

4. What is the mean value of the "emulated area" as n approaches infinity?

Answer 1

For n = 10, Δx = width of each subinterval = (b-a)/10

Right Riemann Sum = ∑_{(i=1 to 10)} ([-5(a+iΔx)+6]Δx)

For n = 100, change 10 to 100 in the above.

As n approaches infinity, the Riemann Sum approaches ∫_{(a to b)} [-5x+6]dx.

Mean value = (1/(b-a))∫_{(a to b)} [-5x+6]dx